hypothesis

In mathematics, a is an unproven statement which is supported by all the available data and by many weaker results. An unproven mathematical statement is usually called a “conjecture”, and while experimentation can sometimes produce millions of examples to support a conjecture, usually nothing short of a proof can convince experts in the field. But when a conjecture is supported not only but all the available data but also by numerous weaker results, it is upgraded in label to a hypothesis. The most famous conjecture in mathematics is the Riemann hypothesis, which despite many attempts at a proof, is supported by many related results. The convexity conjecture, on the other hand, is considered “incompatible” with the $n$-tuples conjecture and more results appear to support the latter, thus neither is upgraded to hypothesis.

References

• 1 R. Crandall & C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001: 1.2.4
Title hypothesis Hypothesis 2013-03-22 17:15:18 2013-03-22 17:15:18 PrimeFan (13766) PrimeFan (13766) 6 PrimeFan (13766) Definition msc 00A05